Piecewise continuous hybrid systems based observer design for linear systems with variable sampling periods and delay output

• The present paper deals with a new continuous undelayed state observer design approach by using only the sampled and delayed measurements where the sampling period and delayed value are variable and unknown.
• This proposed Piecewise Continuous Observer (PCO), which is derived by using the theory of a particular hybrid systems called Piecewise Continuous Hybrid Systems (PCHS), has a very simple structure and can be easily implemented to the networked visual servoing systems.
• This type PCO observer can be also adapted easily according to other kind feedbacks, such as sampled output, delayed output, sampled and delayed state, sampled state, or delayed state whose sampling periods and delayed values are unknown.
• The proposed PCO observer stability is also analyzed and demonstrated. Moreover, to show the proposed PCO observer performance, a comparison with a Lyapunov-Krasovskii technique and descriptor representation based observer is conducted via a numerical example.

The present paper deals with a new continuous undelayed state observer design approach by using only the sampled and delayed measurements where the sampling period and delayed value are variable and unknown. This proposed piecewise continuous observer (PCO), which is derived by using the theory of a particular hybrid systems called piecewise continuous hybrid systems (PCHS), has a very simple structure and can be easily implemented to the networked visual serving systems. This type PCO observer can be also adapted easily according to other kind feedbacks, such as sampled output, delayed output, sampled and delayed state, sampled state, or delayed state whose sampling periods and delayed values are unknown. The proposed PCO observer stability is also analyzed and demonstrated. Moreover, to show the proposed PCO observer performance, a comparison with a Lyapunov–Krasovskii technique and descriptor representation based observer is conducted via a numerical example.